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Block #549,570

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/17/2014, 3:32:50 PM Β· Difficulty 10.9610 Β· 6,258,133 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
a6abbb716c4692e2948c9ee8b4b82803e9f05b6d099af356b63de9e351ac26f5
View on Chainz β†—

Height

#549,570

Difficulty

10.960955

Transactions

2

Size

399 B

Version

2

Bits

0af60124

Nonce

147,362,850

Timestamp

5/17/2014, 3:32:50 PM

Confirmations

6,258,133

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

08c39252273a6fd348c423350f160273da0de41d55b4e532e5ced533bc0b6548
Transactions (2)
Coinbase1a2746d83cdc0f…21ac8e8d11727a
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
ed8fa921aa1835…7b1e632425ba9f
1 in β†’ 1 out3.0067 XPM191 B
AP7DoKhr…5poRYGk3
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.780 Γ— 10⁹⁹(100-digit number)
17809635729135166570…10248400470195976001
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.780 Γ— 10⁹⁹(100-digit number)
17809635729135166570…10248400470195976001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.561 Γ— 10⁹⁹(100-digit number)
35619271458270333140…20496800940391952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.123 Γ— 10⁹⁹(100-digit number)
71238542916540666281…40993601880783904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.424 Γ— 10¹⁰⁰(101-digit number)
14247708583308133256…81987203761567808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.849 Γ— 10¹⁰⁰(101-digit number)
28495417166616266512…63974407523135616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.699 Γ— 10¹⁰⁰(101-digit number)
56990834333232533025…27948815046271232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.139 Γ— 10¹⁰¹(102-digit number)
11398166866646506605…55897630092542464001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.279 Γ— 10¹⁰¹(102-digit number)
22796333733293013210…11795260185084928001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.559 Γ— 10¹⁰¹(102-digit number)
45592667466586026420…23590520370169856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.118 Γ— 10¹⁰¹(102-digit number)
91185334933172052840…47181040740339712001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,705,655 XPMΒ·at block #6,807,702 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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